*2.3. Outcome of the Parameterization*

The physical parameters in Equations (12) and (13) are radiation *Rd*; the Prandtl number Pr; the local Reynolds numbers Re*s* and Re*b*; the material parameter of the Sisko fluid, *B*1; the magnetic parameter *M*; the radius of curvature *B*; the thermal conductivity *<sup>α</sup>f* ; the slip parameter *B*2; and the suction parameter *S*, which are obtained as follows:

 $R\_d = \frac{4\sigma\_1 T\_\infty^3}{k\_1 k\_f},$  $\Pr = \frac{s u\_w}{a\_f}$  $\text{Re}\_b \frac{-2}{\pi + 1}, \text{Re}\_s = \frac{u\_w s}{\nu\_f},$  $\text{Re}\_b = \frac{u\_w^{2-n} s^n \rho\_f}{b},$  $B\_1 = \frac{\text{Re}\_b \frac{2}{n+1}}{\text{Re}\_s},$  $M = \frac{\text{Re}\_b \frac{2}{n+1}}{\text{Re}\_s},$  $B = \frac{k\_f}{\left(\varepsilon\_f \rho\_f\right)\_f},$  $B\_2 = \frac{l\_f}{\zeta}$  $\text{Re}\_b \frac{1}{n+1},$  $S = \frac{-v\_0}{u\_w} \left(\frac{n+1}{2n}\right)$  $\text{Re}\_b \frac{1}{n+1}.$ 

The boundary conditions are

$$\begin{cases} \quad F'(0) = \lambda + B\_2 \Big(F''(0) - \frac{F'(0)}{B}\Big), F(0) = S, \theta(0) = 1 \text{ at } \eta = 0, \\\quad F'(\infty) \to 0, F''(\infty) \to 0, \theta(\infty) \to 0 \text{ as } \eta \to \infty. \end{cases} \tag{14}$$

The pressure term can be obtained from Equation (11), which becomes:

$$P = \frac{\left(\eta + B\right)\frac{\rho\_{nf}}{\rho\_f}}{2B} \left[ \begin{array}{c} \frac{B}{\eta + B} \left(\frac{2\eta}{n+1}\right) \left(FF'' + \frac{FF'}{\eta + B}\right) - \frac{B}{\eta + B}F'^2 + \frac{\frac{\rho\_{nf}}{\rho\_f}}{\frac{\rho\_f}{\rho\_f}}B\_1 \left(\frac{F'' - \frac{F'}{\eta + B}}{\eta + B}\right)^2 + \\\\ \frac{\eta}{\frac{\rho\_f}{\rho\_f}} \left(-\left(F'' - \frac{F'}{\eta + B}\right)\right)^{n-1} \left(F''' - \frac{F''}{\eta + B} + \frac{F'}{\left(\eta + B\right)^2}\right) - \\\\ \frac{2}{\left(\eta + B\right)\frac{\rho\_f}{\rho\_f}} \left(-\left(F'' - \frac{F'}{\eta + B}\right)\right)^n - M\frac{\frac{\rho\_f}{\rho\_f}}{\frac{\rho\_f}{\rho\_f}}F' \end{array} \right] \tag{15}$$
